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arXiv · 2604.26183

Monsky Matrix and 2-Selmer rank

Shamik Das·Sudipa Mondal
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Abstract

In this article, we produce infinite families of non-congruent numbers in the residue class of $1,2,$ and $3$ modulo $8$ with arbitrarily many triples or quadruples prime factors. In short, we use Monsky matrix to show that the $2$-Selmer rank of the corresponding congruent number elliptic curve is zero. We also establish some quantitative results to conclude that each such family contains infinitely many non-congruent numbers.

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Shamik Das, Sudipa Mondal. 2026-04-29. Monsky Matrix and 2-Selmer rank. https://arxiv.org/abs/2604.26183

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